Rewrite a quadratic function to easily see the transformations involved. The instructional task takes a general quadratic function and rewrites it into a form that shows the translations and scaling of the parent quadratic function. The form allows the quadratic formula to be derived easily.

Concepts

quadratic formula, quadratic functions, completing the square, roots, zeros, transformations

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Additional Tags

math

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Instructional Ideas

• For those that struggle with dealing with all the variables, have them work with concrete examples

Classroom Considerations

• The class should be comfortable manipulating variables as opposed to numbers
• Class members should have already completed the previous task, "Building an Explicit Quadratic Function"

Pros

• The solution shows all the steps needed to go from one point to the next
• Includes a connection to another task that uses a similar process

Cons

• None

Common Core

HSA-SSE.B.3.a HSA-SSE.B.4 HSA-REI.B.4.a HSF-BF.B.3